On MacLane-Vaqui\'e key polynomials

Abstract

One of the main goals of this paper is to present the relation of limit key polynomials and limit MacLane-Vaqui\'e key polynomials. This is a continuation of the work started in a paper by Decaup, Mahboub and Spivakovsky, where it is proved the equivalent result for key polynomials (which are not limit). Moreover, we present a result (Theorem 1.1) that generalizes various results in the literature.